For simplicity we have also only considered the simplest form of the ABC algorithm – many other increasingly sophisticated approaches exist, including Markov Chain Monte Carlo algorithms, Sequential Monte Carlo methods [1]} and rare event schemes [2]}. It would be expected that for models with larger numbers of parameters, significant improvements in efficiency could be obtained by applying one of these approaches rather than a rejection sampler based ABC approach. Doing so would not require any changes to the topological aspects of TABC, only the encompassing sampling mechanism.
